jackknifeKME: Jackknife estimates of Kaplan-Meier estimators or integrals

In jackknifeKME: Jackknife Estimates of Kaplan-Meier Estimators or Integrals

Description

This function computes the jackknife estimates of Kaplan-Meier estimators.

Usage

jackknifeKME(X, Y, delta, method = "PDQ", estimator = 1)

Arguments

X	covariate matrix under study, particularly for AFT modelling. The order of matrix covariate is typically n by p. If there is no covariates available then it can be ommitted under only the PDQ method. See last two examples. X must be a matrix of order at least n by 2 under the methods, RcondMean and RcondMedian.
Y	typically the logarithmic of the survival time under AFT models. Otherwise survival time.
delta	status. it includes value 1 for uncensored and value 0 for censored subject.
method	imputing methods for the last largest censored observations under right censoring. The methods satisfy the basic right censoring assumption and also the Efron's redistribution algorithm. For details see Khan and Shaw (2013). One of "condMean (conditional mean)", "condMedian" (conditional median), "RcondMean (resampling based conditional mean)", "RcondMedian (resampling based conditional median)", "PDQ (predicted difference quantity)". Default is "PDQ". Here only "PDQ" method works without covariate (X).
estimator	Kaplan-Meier estimator for the K-th F-moment. 1 for Kaplan-Meier mean lifetime estimator, 2 for Kaplan-Meier estimator for 2nd F-moment. Similarly, for higher order F-moment, value for estimator is used accordingly. Default is 1.

Details

This function computes the jackknife estimates of Kaplan-Meier estimators, the jackknife estimates of bias of Kaplan-Meier estimators, the bias corrected jackknife estimates of Kaplan-Meier estimators. This gives also modified jackknife estimates of bias of Kaplan-Meier estimators, the modified bias corrected jackknife estimates of Kaplan-Meier estimators.

The original jackknife estimate of bias for kaplan-Meier lifetime estimator is nonzero if and only if status of the last largest datum and second to the last largest datum are defined as delta_(n)=1 and delta_(n-1)=0 respectively (Stute and Wang, 1994) i.e., under pair (delta_(n)=1, delta_(n-1)=0). But the modified Kaplan-Meier estimate is nonzero if only delta_(n-1)=0. Furthermore, a modified Kaplan-Meier estimator and its jackknife estimate is developed when (delta_(n)=0, delta_(n-1)=0) (Khan and Shaw, 2015). There are different types of Kaplan-Meier lifetime estimators in practice. In Khan and Shaw (2015) only the mean lifetime estimator and one higher order (say, 2-nd) F-moment estimator are used for illustration purpose.

Value

A "jackknifeKME" object is returned. It includes

km.est	Kaplan-Meier estimate
modkm.est	modified Kaplan-Meier estimate
Jbias.kme	jackknife estimate of bias of Kaplan-Meier estimator
Bcorr.Jkme	bias corrected jackknife estimate of Kaplan-Meier estimator
modJbias.kme	modified jackknife estimate of bias of Kaplan-Meier estimator
Bcorr.modJkme	bias corrected modified jackknife estimate of Kaplan-Meier estimator

Author(s)

Hasinur Rahaman Khan and Ewart Shaw

References

Khan and Shaw (2015) imputeYn: Imputing the last largest censored observation/observations under weighted least squares. R package version 1.3, https://cran.r-project.org/package=imputeYn.

Khan and Shaw. (2013). On Dealing with Censored Largest Observations under Weighted Least Squares. CRiSM working paper, Department of Statistics, University of Warwick, UK, No. 13-07. Also available in http://arxiv.org/abs/1312.2533.

Khan and Shaw. (2015). Robust bias estimation for Kaplan-Meier Survival Estimator with Jackknifing. Journal of Statistical Theory and Practice, (published online; DOI:10.1080/15598608.2015.1062833). Also available in http://arxiv.org/abs/1312.4058.

Stute, W. and Wang, J. (1994). The jackknife estimate of a Kaplan-Meier integral. Biometrika 81, 602-606.

Examples

#For full data typically used for AFT models (using imputeYn (2015) package). 
#For mean lifetime estimator.
data<-data(n=100, p=4, r=0, b1=c(2,2,3,3), sig=1, Cper=0)
kme1<-jackknifeKME(data$x,data$y, data$delta, method="condMean",estimator = 1)
kme1

#Estimates are for mean lifetime estimators.Data contain only status and survival time.  
data2<-simdata(n = 100,lambda = 2.04) 
data2$delta[length(data2$delta)]<-0 
kme2<-jackknifeKME(, data2$Y, data2$delta, method="PDQ",estimator = 1)
kme2

#Estimates are for Kaplan-Meier 2nd order F-moment.
data3<-simdata(n = 100,lambda = 2.04) 
data3$delta[length(data3$delta)]<-0 
kme3<-jackknifeKME(, data3$Y, data3$delta, method="PDQ",estimator = 2)
kme3

Example output

Loading required package: imputeYn
Loading required package: quadprog
Loading required package: emplik
Loading required package: mvtnorm
Loading required package: survival
Loading required package: boot

Attaching package: 'boot'

The following object is masked from 'package:survival':

    aml


Attaching package: 'imputeYn'

The following object is masked from 'package:utils':

    data

$km.est
[1] 4.373432

$modkm.est
[1] 4.373432

$Jbias.kme
[1] 0

$Bcorr.Jkme
[1] 4.373432

$modJbias.kme
[1] -0.3432863

$Bcorr.modJkme
[1] 4.716718

attr(,"class")
[1] "jacknifeKME"
$km.est
[1] 1.10007

$modkm.est
[1] 1.10007

$Jbias.kme
[1] 0

$Bcorr.Jkme
[1] 1.10007

$modJbias.kme
numeric(0)

$Bcorr.modJkme
numeric(0)

attr(,"class")
[1] "jacknifeKME"
$km.est
[1] 3.261398

$modkm.est
[1] 3.261398

$Jbias.kme
[1] 0

$Bcorr.Jkme
[1] 3.261398

$modJbias.kme
numeric(0)

$Bcorr.modJkme
numeric(0)

attr(,"class")
[1] "jacknifeKME"

jackknifeKME documentation built on May 2, 2019, 5:27 a.m.